for some arbitrary functions
\((a_k,b_k)\) ,
and for all
\(k=1,\ldots ,n\) 
[1]}, [2]}.
For any choice of \((a_k,b_k)\) , the
rearrangement \(U\)  is a strictly
monotone (increasing) triangular map, since
\(\partial _k \,U^k = \exp (b_k)>0\)  for all \(k\) .
In fact, (REF ) provides
a rather general way to represent monotone
triangular functions.
